Place potatoes in a large saucepan; cover with cold water to a depth of 2 inches; add salt. Bring to a simmer over medium; cook until potatoes are fork-tender, about 14 minutes. Drain and return potatoes to saucepan. Shake saucepan over medium heat to dry potatoes, about 1 minute.
Preheat oven to 425°F. Line 2 large baking sheets using parchment paper. Mash potatoes and 2 tablespoons of the butter until smooth. Add pecorino cheese, cream, black pepper, and nutmeg; mash potatoes until incorporated. Let potatoes cool until warm to the touch, 3 to 5 minutes. Stir in egg yolks, 1 at a time, stirring until incorporated.
Transfer potato mixture to a pastry bag fitted with a 1/2-inch star tip; pipe potatoes in even rosettes about 2 inches wide and 2 inches high onto prepared baking sheets. Lightly brush with remaining 2 tablespoons melted butter.
Bake in preheated oven until golden brown, about 20 minutes. Top with chives. Serve hot.
